Consider the following two-player game: starting with the single number 123, two players alternately subtract numbers from the set {1, 2, 3} from this value. the player who first gets this sum to 0 wins. if you want to win this game, should you go first or second? prove that your chosen player has a winning strategy

Suppose you are an ad-serving company and you maintain a log of cookie data for ads you serve to the web pages for a particular vendor (say amazon). a. how can you use this data to determine which are the best ads? b. how can you use this data to determine which are the best ad formats? c. how could you records of past ads and ad clicks to determine which ads to send to a given ip address? d. how could you use this data to determine how well the technique you used in your answer to part c was working? e. how could you use this data to determine that a given ip address is used by more than one person? f. how does having this data give you a competitive advantage vis-à-vis other ad-serving companies?